Immune system responses are elicited in several different situations. The most frequent response involves protection against infectious microorganisms. An undesirable immune response can occur, however, following transplantation of foreign tissue, or in an autoimmune disease in which the body's own antigens become targets for the immune response. In order to initiate an antigen-specific response, a T cell must receive at least two discrete signals delivered by an antigen-presenting cell (APC). The first signal is antigen-specific, and is provided when the T cell receptor (TCR) interacts with an antigen in the context of a major histocompatibility complex (MHC) protein, or an MHC-related CD1 protein, that is expressed on the surface of an APC. The second, costimulatory, signal involves the interaction of a T cell surface antigen with its ligand on the APC. For example, the costimulatory molecule receptors CD28 and/or CTLA-4 (expressed on T cells) must interact with their ligands, B7-1 and/or B7-2 (expressed on APC), in order to achieve optimal activation of T cells that have been stimulated by MHC/peptide complexes expressed on APC. ICOS is an inducible T cell costimulatory receptor molecule that displays some homology to CD28 and CTLA-4, and interacts with B7-H2 expressed on the surface of APC. ICOS and B7-H2 have been implicated in the regulation of cell-mediated and humoral immune responses. Costimulatory molecules with altered binding affinities for their ligands would be useful for modulating the level of T cell activation and proliferation, and could be used either to boost the level of desired immune responses or to reduce the level of undesirable immune responses, as appropriate.